LMFDB - Embedded newform 648.2.l.g.107.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(107,648)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("648.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.23
Character	$\chi$	$=$	648.107
Dual form			648.2.l.g.539.23

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40154 + 0.188930i) q^{2} +(1.92861 + 0.529584i) q^{4} +(0.474833 + 0.822435i) q^{5} +(4.07898 + 2.35500i) q^{7} +(2.60297 + 1.10660i) q^{8} +O(q^{10})$	\(q+(1.40154 + 0.188930i) q^{2} +(1.92861 + 0.529584i) q^{4} +(0.474833 + 0.822435i) q^{5} +(4.07898 + 2.35500i) q^{7} +(2.60297 + 1.10660i) q^{8} +(0.510114 + 1.24238i) q^{10} +(-3.72007 - 2.14778i) q^{11} +(-3.52349 + 2.03429i) q^{13} +(5.27191 + 4.07126i) q^{14} +(3.43908 + 2.04272i) q^{16} -1.19178i q^{17} -3.17693 q^{19} +(0.480220 + 1.83762i) q^{20} +(-4.80803 - 3.71303i) q^{22} +(-0.375325 - 0.650083i) q^{23} +(2.04907 - 3.54909i) q^{25} +(-5.32263 + 2.18544i) q^{26} +(6.61959 + 6.70204i) q^{28} +(3.87181 - 6.70617i) q^{29} +(0.496917 - 0.286895i) q^{31} +(4.43407 + 3.51270i) q^{32} +(0.225163 - 1.67032i) q^{34} +4.47293i q^{35} +4.87320i q^{37} +(-4.45258 - 0.600216i) q^{38} +(0.325864 + 2.66622i) q^{40} +(-8.45135 + 4.87939i) q^{41} +(2.65770 - 4.60327i) q^{43} +(-6.03713 - 6.11233i) q^{44} +(-0.403212 - 0.982025i) q^{46} +(4.91012 - 8.50458i) q^{47} +(7.59204 + 13.1498i) q^{49} +(3.54237 - 4.58705i) q^{50} +(-7.87276 + 2.05736i) q^{52} +0.877682 q^{53} -4.07935i q^{55} +(8.01139 + 10.6438i) q^{56} +(6.69348 - 8.66745i) q^{58} +(1.51936 - 0.877204i) q^{59} +(8.59196 + 4.96057i) q^{61} +(0.750651 - 0.308212i) q^{62} +(5.55086 + 5.76090i) q^{64} +(-3.34614 - 1.93189i) q^{65} +(-5.48335 - 9.49744i) q^{67} +(0.631147 - 2.29848i) q^{68} +(-0.845069 + 6.26897i) q^{70} -9.91048 q^{71} +8.74944 q^{73} +(-0.920692 + 6.82996i) q^{74} +(-6.12706 - 1.68245i) q^{76} +(-10.1160 - 17.5215i) q^{77} +(-4.97571 - 2.87273i) q^{79} +(-0.0470178 + 3.79837i) q^{80} +(-12.7667 + 5.24193i) q^{82} +(-10.8283 - 6.25173i) q^{83} +(0.980161 - 0.565896i) q^{85} +(4.59456 - 5.94953i) q^{86} +(-7.30646 - 9.70724i) q^{88} -10.1440i q^{89} -19.1630 q^{91} +(-0.379583 - 1.45252i) q^{92} +(8.48848 - 10.9918i) q^{94} +(-1.50851 - 2.61282i) q^{95} +(-3.91511 + 6.78118i) q^{97} +(8.15614 + 19.8643i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{16} + 12 q^{22} - 24 q^{25} + 24 q^{28} + 24 q^{34} + 24 q^{40} - 24 q^{46} + 24 q^{49} + 12 q^{58} + 48 q^{64} - 48 q^{67} + 36 q^{70} + 60 q^{76} - 72 q^{82} + 60 q^{88} - 48 q^{94}+O(q^{100}) $ 48 * q - 12 * q^16 + 12 * q^22 - 24 * q^25 + 24 * q^28 + 24 * q^34 + 24 * q^40 - 24 * q^46 + 24 * q^49 + 12 * q^58 + 48 * q^64 - 48 * q^67 + 36 * q^70 + 60 * q^76 - 72 * q^82 + 60 * q^88 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.40154	+	0.188930i	0.991036	+	0.133594i
$2$	1.40154	+	0.188930i	0.991036	+	0.133594i
$3$		0			0
$3$		0			0
$4$	1.92861	+	0.529584i	0.964306	+	0.264792i
$5$	0.474833	+	0.822435i	0.212352	+	0.367804i	0.952450	−	0.304695i	$-0.0985544\pi$
$5$	0.474833	+	0.822435i	0.212352	+	0.367804i	−0.740098	+	0.672499i	$0.765221\pi$
$6$		0			0
$7$	4.07898	+	2.35500i	1.54171	+	0.890106i	0.998731	+	0.0503587i	$0.0160365\pi$
$7$	4.07898	+	2.35500i	1.54171	+	0.890106i	0.542978	+	0.839747i	$0.317297\pi$
$8$	2.60297	+	1.10660i	0.920287	+	0.391243i
$9$		0			0
$10$	0.510114	+	1.24238i	0.161312	+	0.392876i
$11$	−3.72007	−	2.14778i	−1.12164	−	0.647581i	−0.179823	−	0.983699i	$-0.557552\pi$
$11$	−3.72007	−	2.14778i	−1.12164	−	0.647581i	−0.941820	+	0.336118i	$0.890886\pi$
$12$		0			0
$13$	−3.52349	+	2.03429i	−0.977240	+	0.564210i	−0.901436	−	0.432913i	$-0.857486\pi$
$13$	−3.52349	+	2.03429i	−0.977240	+	0.564210i	−0.0758039	+	0.997123i	$0.524152\pi$
$14$	5.27191	+	4.07126i	1.40898	+	1.08809i
$15$		0			0
$16$	3.43908	+	2.04272i	0.859770	+	0.510681i
$17$		−	1.19178i		−	0.289049i	−0.989501	−	0.144524i	$-0.953835\pi$
$17$		−	1.19178i		−	0.289049i	0.989501	−	0.144524i	$-0.0461652\pi$
$18$		0			0
$19$	−3.17693			−0.728837			−0.364418	−	0.931235i	$-0.618732\pi$
$19$	−3.17693			−0.728837			−0.364418	+	0.931235i	$0.618732\pi$
$20$	0.480220	+	1.83762i	0.107380	+	0.410905i
$21$		0			0
$22$	−4.80803	−	3.71303i	−1.02508	−	0.791620i
$23$	−0.375325	−	0.650083i	−0.0782608	−	0.135552i	0.824239	−	0.566242i	$-0.191603\pi$
$23$	−0.375325	−	0.650083i	−0.0782608	−	0.135552i	−0.902500	+	0.430691i	$0.858270\pi$
$24$		0			0
$25$	2.04907	−	3.54909i	0.409813	−	0.709818i
$26$	−5.32263	+	2.18544i	−1.04385	+	0.428599i
$27$		0			0
$28$	6.61959	+	6.70204i	1.25099	+	1.26657i
$29$	3.87181	−	6.70617i	0.718977	−	1.24530i	−0.242428	−	0.970169i	$-0.577944\pi$
$29$	3.87181	−	6.70617i	0.718977	−	1.24530i	0.961405	−	0.275136i	$-0.0887227\pi$
$30$		0			0
$31$	0.496917	−	0.286895i	0.0892490	−	0.0515279i	−0.454711	−	0.890639i	$-0.650258\pi$
$31$	0.496917	−	0.286895i	0.0892490	−	0.0515279i	0.543960	+	0.839111i	$0.316924\pi$
$32$	4.43407	+	3.51270i	0.783840	+	0.620963i
$33$		0			0
$34$	0.225163	−	1.67032i	0.0386151	−	0.286458i
$35$			4.47293i			0.756062i
$36$		0			0
$37$			4.87320i			0.801148i	0.916264	+	0.400574i	$0.131189\pi$
$37$			4.87320i			0.801148i	−0.916264	+	0.400574i	$0.868811\pi$
$38$	−4.45258	−	0.600216i	−0.722304	−	0.0973679i
$39$		0			0
$40$	0.325864	+	2.66622i	0.0515237	+	0.421567i
$41$	−8.45135	+	4.87939i	−1.31988	+	0.762032i	−0.983709	−	0.179769i	$-0.942465\pi$
$41$	−8.45135	+	4.87939i	−1.31988	+	0.762032i	−0.336170	+	0.941801i	$0.609132\pi$
$42$		0			0
$43$	2.65770	−	4.60327i	0.405295	−	0.701992i	−0.589060	−	0.808089i	$-0.700502\pi$
$43$	2.65770	−	4.60327i	0.405295	−	0.701992i	0.994356	+	0.106097i	$0.0338353\pi$
$44$	−6.03713	−	6.11233i	−0.910132	−	0.921468i
$45$		0			0
$46$	−0.403212	−	0.982025i	−0.0594504	−	0.144792i
$47$	4.91012	−	8.50458i	0.716214	−	1.24052i	−0.246275	−	0.969200i	$-0.579207\pi$
$47$	4.91012	−	8.50458i	0.716214	−	1.24052i	0.962489	−	0.271320i	$-0.0874601\pi$
$48$		0			0
$49$	7.59204	+	13.1498i	1.08458	+	1.87854i
$50$	3.54237	−	4.58705i	0.500967	−	0.648707i
$51$		0			0
$52$	−7.87276	+	2.05736i	−1.09176	+	0.285305i
$53$	0.877682			0.120559			0.0602794	−	0.998182i	$-0.480801\pi$
$53$	0.877682			0.120559			0.0602794	+	0.998182i	$0.480801\pi$
$54$		0			0
$55$		−	4.07935i		−	0.550060i
$56$	8.01139	+	10.6438i	1.07057	+	1.42234i
$57$		0			0
$58$	6.69348	−	8.66745i	0.878897	−	1.13809i
$59$	1.51936	−	0.877204i	0.197804	−	0.114202i	−0.397827	−	0.917461i	$-0.630235\pi$
$59$	1.51936	−	0.877204i	0.197804	−	0.114202i	0.595631	+	0.803258i	$0.296902\pi$
$60$		0			0
$61$	8.59196	+	4.96057i	1.10009	+	0.635136i	0.936244	−	0.351350i	$-0.114277\pi$
$61$	8.59196	+	4.96057i	1.10009	+	0.635136i	0.163844	+	0.986486i	$0.447611\pi$
$62$	0.750651	−	0.308212i	0.0953328	−	0.0391429i
$63$		0			0
$64$	5.55086	+	5.76090i	0.693857	+	0.720113i
$65$	−3.34614	−	1.93189i	−0.415037	−	0.239622i
$66$		0			0
$67$	−5.48335	−	9.49744i	−0.669898	−	1.16030i	−0.977932	−	0.208922i	$-0.933005\pi$
$67$	−5.48335	−	9.49744i	−0.669898	−	1.16030i	0.308034	−	0.951375i	$-0.400329\pi$
$68$	0.631147	−	2.29848i	0.0765378	−	0.278731i
$69$		0			0
$70$	−0.845069	+	6.26897i	−0.101005	+	0.749285i
$71$	−9.91048			−1.17616			−0.588079	−	0.808804i	$-0.700116\pi$
$71$	−9.91048			−1.17616			−0.588079	+	0.808804i	$0.700116\pi$
$72$		0			0
$73$	8.74944			1.02404			0.512022	−	0.858972i	$-0.328897\pi$
$73$	8.74944			1.02404			0.512022	+	0.858972i	$0.328897\pi$
$74$	−0.920692	+	6.82996i	−0.107028	+	0.793967i
$75$		0			0
$76$	−6.12706	−	1.68245i	−0.702822	−	0.192990i
$77$	−10.1160	−	17.5215i	−1.15283	−	1.99676i
$78$		0			0
$79$	−4.97571	−	2.87273i	−0.559811	−	0.323207i	0.193259	−	0.981148i	$-0.438094\pi$
$79$	−4.97571	−	2.87273i	−0.559811	−	0.323207i	−0.753070	+	0.657941i	$0.771428\pi$
$80$	−0.0470178	+	3.79837i	−0.00525675	+	0.424671i
$81$		0			0
$82$	−12.7667	+	5.24193i	−1.40985	+	0.578874i
$83$	−10.8283	−	6.25173i	−1.18856	−	0.686217i	−0.230583	−	0.973053i	$-0.574063\pi$
$83$	−10.8283	−	6.25173i	−1.18856	−	0.686217i	−0.957980	+	0.286836i	$0.907397\pi$
$84$		0			0
$85$	0.980161	−	0.565896i	0.106313	−	0.0613800i
$86$	4.59456	−	5.94953i	0.495444	−	0.641555i
$87$		0			0
$88$	−7.30646	−	9.70724i	−0.778872	−	1.03480i
$89$		−	10.1440i		−	1.07527i	−0.843179	−	0.537633i	$-0.819319\pi$
$89$		−	10.1440i		−	1.07527i	0.843179	−	0.537633i	$-0.180681\pi$
$90$		0			0
$91$	−19.1630			−2.00882
$92$	−0.379583	−	1.45252i	−0.0395743	−	0.151436i
$93$		0			0
$94$	8.48848	−	10.9918i	0.875520	−	1.13372i
$95$	−1.50851	−	2.61282i	−0.154770	−	0.268069i
$96$		0			0
$97$	−3.91511	+	6.78118i	−0.397520	+	0.688524i	−0.993419	−	0.114535i	$-0.963462\pi$
$97$	−3.91511	+	6.78118i	−0.397520	+	0.688524i	0.595900	+	0.803059i	$0.296796\pi$
$98$	8.15614	+	19.8643i	0.823894	+	2.00660i
$99$		0			0
$100$	5.83139	−	5.75966i	0.583139	−	0.575966i
$101$	−8.92656	+	15.4613i	−0.888226	+	1.53845i	−0.0462544	+	0.998930i	$0.514728\pi$
$101$	−8.92656	+	15.4613i	−0.888226	+	1.53845i	−0.841971	+	0.539522i	$0.818605\pi$
$102$		0			0
$103$	−2.12533	+	1.22706i	−0.209415	+	0.120906i	−0.601040	−	0.799219i	$-0.705247\pi$
$103$	−2.12533	+	1.22706i	−0.209415	+	0.120906i	0.391624	+	0.920125i	$0.371913\pi$
$104$	−11.4227	+	1.39607i	−1.12008	+	0.136896i
$105$		0			0
$106$	1.23010	+	0.165820i	0.119478	+	0.0161059i
$107$			0.283208i			0.0273788i	0.999906	+	0.0136894i	$0.00435760\pi$
$107$			0.283208i			0.0273788i	−0.999906	+	0.0136894i	$0.995642\pi$
$108$		0			0
$109$		−	9.74716i		−	0.933609i	−0.884361	−	0.466805i	$-0.845405\pi$
$109$		−	9.74716i		−	0.933609i	0.884361	−	0.466805i	$-0.154595\pi$
$110$	0.770711	−	5.71736i	0.0734844	−	0.545129i
$111$		0			0
$112$	9.21733	+	16.4313i	0.870955	+	1.55261i
$113$	−4.09400	+	2.36367i	−0.385131	+	0.222356i	−0.680048	−	0.733167i	$-0.738041\pi$
$113$	−4.09400	+	2.36367i	−0.385131	+	0.222356i	0.294917	+	0.955523i	$0.404708\pi$
$114$		0			0
$115$	0.356434	−	0.617362i	0.0332376	−	0.0575693i
$116$	11.0187	−	10.8831i	1.02306	−	1.01047i
$117$		0			0
$118$	2.29517	−	0.942381i	0.211288	−	0.0867532i
$119$	2.80664	−	4.86124i	0.257284	−	0.445629i
$120$		0			0
$121$	3.72594	+	6.45351i	0.338721	+	0.586683i
$122$	11.1048	+	8.57570i	1.00538	+	0.776407i
$123$		0			0
$124$	1.11030	−	0.290150i	0.0997075	−	0.0260562i
$125$	8.64019			0.772802
$126$		0			0
$127$		−	13.8042i		−	1.22492i	−0.790500	−	0.612462i	$-0.790179\pi$
$127$		−	13.8042i		−	1.22492i	0.790500	−	0.612462i	$-0.209821\pi$
$128$	6.69132	+	9.12284i	0.591435	+	0.806353i
$129$		0			0
$130$	−4.32474	−	3.33980i	−0.379305	−	0.292920i
$131$	−4.10031	+	2.36731i	−0.358245	+	0.206833i	−0.668311	−	0.743882i	$-0.732982\pi$
$131$	−4.10031	+	2.36731i	−0.358245	+	0.206833i	0.310065	+	0.950715i	$0.399649\pi$
$132$		0			0
$133$	−12.9586	−	7.48166i	−1.12365	−	0.648742i
$134$	−5.89077	−	14.3470i	−0.508885	−	1.23939i
$135$		0			0
$136$	1.31883	−	3.10216i	0.113088	−	0.266008i
$137$	13.4704	+	7.77716i	1.15086	+	0.664448i	0.949096	−	0.314987i	$-0.102000\pi$
$137$	13.4704	+	7.77716i	1.15086	+	0.664448i	0.201762	+	0.979435i	$0.435333\pi$
$138$		0			0
$139$	−3.94490	−	6.83276i	−0.334602	−	0.579547i	0.648806	−	0.760953i	$-0.275268\pi$
$139$	−3.94490	−	6.83276i	−0.334602	−	0.579547i	−0.983408	+	0.181406i	$0.941935\pi$
$140$	−2.36879	+	8.62653i	−0.200199	+	0.729075i
$141$		0			0
$142$	−13.8899	−	1.87238i	−1.16561	−	0.157127i
$143$	17.4768			1.46148
$144$		0			0
$145$	7.35385			0.610704
$146$	12.2627	+	1.65303i	1.01486	+	0.136806i
$147$		0			0
$148$	−2.58077	+	9.39850i	−0.212138	+	0.772552i
$149$	8.00344	+	13.8624i	0.655667	+	1.13565i	0.981726	+	0.190300i	$0.0609459\pi$
$149$	8.00344	+	13.8624i	0.655667	+	1.13565i	−0.326059	+	0.945350i	$0.605721\pi$
$150$		0			0
$151$	−1.57918	−	0.911739i	−0.128512	−	0.0741962i	0.434366	−	0.900736i	$-0.356972\pi$
$151$	−1.57918	−	0.911739i	−0.128512	−	0.0741962i	−0.562878	+	0.826540i	$0.690306\pi$
$152$	−8.26943	−	3.51560i	−0.670739	−	0.285153i
$153$		0			0
$154$	−10.8677	−	26.4683i	−0.875743	−	2.13287i
$155$	0.471905	+	0.272455i	0.0379044	+	0.0218841i
$156$		0			0
$157$	−17.7438	+	10.2444i	−1.41611	+	0.817589i	−0.995954	−	0.0898651i	$-0.971356\pi$
$157$	−17.7438	+	10.2444i	−1.41611	+	0.817589i	−0.420152	+	0.907454i	$0.638023\pi$
$158$	−6.43090	−	4.96629i	−0.511615	−	0.395097i
$159$		0			0
$160$	−0.783523	+	5.31468i	−0.0619429	+	0.420162i
$161$		−	3.53556i		−	0.278641i
$162$		0			0
$163$	−7.59374			−0.594787			−0.297394	−	0.954755i	$-0.596117\pi$
$163$	−7.59374			−0.594787			−0.297394	+	0.954755i	$0.596117\pi$
$164$	−18.8834	+	4.93474i	−1.47455	+	0.385339i
$165$		0			0
$166$	−13.9952	−	10.8078i	−1.08623	−	0.838850i
$167$	2.80664	+	4.86124i	0.217184	+	0.376174i	0.953946	−	0.299978i	$-0.0969794\pi$
$167$	2.80664	+	4.86124i	0.217184	+	0.376174i	−0.736762	+	0.676152i	$0.763646\pi$
$168$		0			0
$169$	1.77664	−	3.07723i	0.136665	−	0.236710i
$170$	1.48065	−	0.607943i	0.113560	−	0.0466271i
$171$		0			0
$172$	7.56349	−	7.47044i	0.576711	−	0.569616i
$173$	6.31622	−	10.9400i	0.480214	−	0.831754i	−0.519529	−	0.854453i	$-0.673892\pi$
$173$	6.31622	−	10.9400i	0.480214	−	0.831754i	0.999742	+	0.0226986i	$0.00722582\pi$
$174$		0			0
$175$	16.7162	−	9.65110i	1.26363	−	0.729555i
$176$	−8.40629	−	14.9855i	−0.633648	−	1.12957i
$177$		0			0
$178$	1.91651	−	14.2172i	0.143649	−	1.06563i
$179$			20.5282i			1.53435i	0.641439	+	0.767174i	$0.278338\pi$
$179$			20.5282i			1.53435i	−0.641439	+	0.767174i	$0.721662\pi$
$180$		0			0
$181$			9.96062i			0.740367i	0.928959	+	0.370184i	$0.120705\pi$
$181$			9.96062i			0.740367i	−0.928959	+	0.370184i	$0.879295\pi$
$182$	−26.8576	−	3.62046i	−1.99082	−	0.268366i
$183$		0			0
$184$	−0.257575	−	2.10748i	−0.0189887	−	0.155365i
$185$	−4.00789	+	2.31395i	−0.294666	+	0.170125i
$186$		0			0
$187$	−2.55968	+	4.43350i	−0.187182	+	0.324210i
$188$	13.9736	−	13.8017i	1.01913	−	1.00659i
$189$		0			0
$190$	−1.62059	−	3.94696i	−0.117570	−	0.286343i
$191$	−11.4999	+	19.9185i	−0.832105	+	1.44125i	0.0642603	+	0.997933i	$0.479531\pi$
$191$	−11.4999	+	19.9185i	−0.832105	+	1.44125i	−0.896366	+	0.443316i	$0.853802\pi$
$192$		0			0
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$	−6.76834	+	8.76439i	−0.485939	+	0.629246i
$195$		0			0
$196$	7.67817	+	29.3815i	0.548441	+	2.09868i
$197$	0.519639			0.0370228			0.0185114	−	0.999829i	$-0.494107\pi$
$197$	0.519639			0.0370228			0.0185114	+	0.999829i	$0.494107\pi$
$198$		0			0
$199$			0.630646i			0.0447053i	0.999750	+	0.0223527i	$0.00711567\pi$
$199$			0.630646i			0.0447053i	−0.999750	+	0.0223527i	$0.992884\pi$
$200$	9.26109	−	6.97065i	0.654858	−	0.492899i
$201$		0			0
$202$	−15.4320	+	19.9830i	−1.08579	+	1.40600i
$203$	31.5861	−	18.2362i	2.21691	−	1.27993i
$204$		0			0
$205$	−8.02596	−	4.63379i	−0.560557	−	0.323638i
$206$	−3.21056	+	1.31823i	−0.223690	+	0.0918457i
$207$		0			0
$208$	−16.2730	−	0.201434i	−1.12833	−	0.0139669i
$209$	11.8184	+	6.82335i	0.817495	+	0.471981i
$210$		0			0
$211$	−4.95897	−	8.58918i	−0.341389	−	0.591304i	0.643302	−	0.765613i	$-0.277564\pi$
$211$	−4.95897	−	8.58918i	−0.341389	−	0.591304i	−0.984691	+	0.174309i	$0.944231\pi$
$212$	1.69271	+	0.464806i	0.116256	+	0.0319230i
$213$		0			0
$214$	−0.0535065	+	0.396927i	−0.00365763	+	0.0271334i
$215$	5.04785			0.344261
$216$		0			0
$217$	2.70255			0.183461
$218$	1.84153	−	13.6610i	0.124724	−	0.925240i
$219$		0			0
$220$	2.16036	−	7.86748i	0.145651	−	0.530426i
$221$	2.42442	+	4.19922i	0.163084	+	0.282470i
$222$		0			0
$223$	6.15507	+	3.55363i	0.412174	+	0.237969i	0.691723	−	0.722162i	$-0.256852\pi$
$223$	6.15507	+	3.55363i	0.412174	+	0.237969i	−0.279549	+	0.960131i	$0.590185\pi$
$224$	9.81407	+	24.7704i	0.655730	+	1.65504i
$225$		0			0
$226$	−6.18446	+	2.53929i	−0.411384	+	0.168911i
$227$	10.7925	+	6.23105i	0.716323	+	0.413569i	0.813398	−	0.581708i	$-0.197615\pi$
$227$	10.7925	+	6.23105i	0.716323	+	0.413569i	−0.0970749	+	0.995277i	$0.530949\pi$
$228$		0			0
$229$	8.45996	−	4.88436i	0.559050	−	0.322768i	−0.193714	−	0.981058i	$-0.562053\pi$
$229$	8.45996	−	4.88436i	0.559050	−	0.322768i	0.752764	+	0.658290i	$0.228720\pi$
$230$	0.616193	−	0.797914i	0.0406306	−	0.0526129i
$231$		0			0
$232$	17.4993	−	13.1714i	1.14888	−	0.864743i
$233$		−	4.66388i		−	0.305541i	−0.988262	−	0.152771i	$-0.951180\pi$
$233$		−	4.66388i		−	0.305541i	0.988262	−	0.152771i	$-0.0488196\pi$
$234$		0			0
$235$	9.32595			0.608358
$236$	3.39481	−	0.887156i	0.220983	−	0.0577489i
$237$		0			0
$238$	4.85204	−	6.28295i	0.314511	−	0.407263i
$239$	1.71266	+	2.96641i	0.110783	+	0.191881i	0.916086	−	0.400982i	$-0.131331\pi$
$239$	1.71266	+	2.96641i	0.110783	+	0.191881i	−0.805303	+	0.592863i	$0.797998\pi$
$240$		0			0
$241$	−0.627860	+	1.08748i	−0.0404440	+	0.0700510i	−0.885539	−	0.464565i	$-0.846211\pi$
$241$	−0.627860	+	1.08748i	−0.0404440	+	0.0700510i	0.845095	+	0.534616i	$0.179544\pi$
$242$	4.00278	+	9.74877i	0.257308	+	0.626675i
$243$		0			0
$244$	13.9435	+	14.1172i	0.892642	+	0.903760i
$245$	−7.20990	+	12.4879i	−0.460624	+	0.797824i
$246$		0			0
$247$	11.1939	−	6.46278i	0.712248	−	0.411217i
$248$	1.61094	−	0.196888i	0.102295	−	0.0125024i
$249$		0			0
$250$	12.1095	+	1.63239i	0.765875	+	0.103241i
$251$		−	20.2340i		−	1.27716i	−0.769556	−	0.638579i	$-0.779523\pi$
$251$		−	20.2340i		−	1.27716i	0.769556	−	0.638579i	$-0.220477\pi$
$252$		0			0
$253$			3.22447i			0.202721i
$254$	2.60802	−	19.3471i	0.163642	−	1.21394i
$255$		0			0
$256$	7.65456	+	14.0502i	0.478410	+	0.878137i
$257$	1.01857	−	0.588069i	0.0635364	−	0.0366828i	−0.467895	−	0.883784i	$-0.654988\pi$
$257$	1.01857	−	0.588069i	0.0635364	−	0.0366828i	0.531432	+	0.847101i	$0.321654\pi$
$258$		0			0
$259$	−11.4764	+	19.8777i	−0.713107	+	1.23514i
$260$	−5.43030	−	5.49793i	−0.336773	−	0.340967i
$261$		0			0
$262$	−6.19399	+	2.54321i	−0.382666	+	0.157120i
$263$	−3.51217	+	6.08325i	−0.216570	+	0.375109i	−0.953757	−	0.300579i	$-0.902820\pi$
$263$	−3.51217	+	6.08325i	−0.216570	+	0.375109i	0.737187	+	0.675688i	$0.236153\pi$
$264$		0			0
$265$	0.416752	+	0.721836i	0.0256009	+	0.0443420i
$266$	−16.7485	−	12.9341i	−1.02691	−	0.793040i
$267$		0			0
$268$	−5.54556	−	21.2208i	−0.338749	−	1.29626i
$269$	−11.4172			−0.696119			−0.348060	−	0.937472i	$-0.613159\pi$
$269$	−11.4172			−0.696119			−0.348060	+	0.937472i	$0.613159\pi$
$270$		0			0
$271$			10.9905i			0.667625i	0.942639	+	0.333813i	$0.108335\pi$
$271$			10.9905i			0.667625i	−0.942639	+	0.333813i	$0.891665\pi$
$272$	2.43447	−	4.09862i	0.147612	−	0.248516i
$273$		0			0
$274$	17.4100	+	13.4450i	1.05178	+	0.812239i
$275$	−15.2453	+	8.80190i	−0.919328	+	0.530775i
$276$		0			0
$277$	3.11917	+	1.80085i	0.187413	+	0.108203i	0.590771	−	0.806839i	$-0.298824\pi$
$277$	3.11917	+	1.80085i	0.187413	+	0.108203i	−0.403358	+	0.915042i	$0.632157\pi$
$278$	−4.23801	−	10.3217i	−0.254179	−	0.619053i
$279$		0			0
$280$	−4.94976	+	11.6429i	−0.295804	+	0.695795i
$281$	−10.6296	−	6.13703i	−0.634111	−	0.366104i	0.148231	−	0.988953i	$-0.452642\pi$
$281$	−10.6296	−	6.13703i	−0.634111	−	0.366104i	−0.782343	+	0.622848i	$0.785975\pi$
$282$		0			0
$283$	1.27237	+	2.20381i	0.0756344	+	0.131003i	0.901362	−	0.433066i	$-0.142568\pi$
$283$	1.27237	+	2.20381i	0.0756344	+	0.131003i	−0.825728	+	0.564069i	$0.809235\pi$
$284$	−19.1135	−	5.24843i	−1.13418	−	0.311437i
$285$		0			0
$286$	24.4944	+	3.30189i	1.44838	+	0.195245i
$287$	−45.9638			−2.71316
$288$		0			0
$289$	15.5797			0.916451
$290$	10.3067	+	1.38936i	0.605230	+	0.0815861i
$291$		0			0
$292$	16.8743	+	4.63356i	0.987491	+	0.271159i
$293$	0.929672	+	1.61024i	0.0543120	+	0.0940712i	0.891903	−	0.452226i	$-0.149370\pi$
$293$	0.929672	+	1.61024i	0.0543120	+	0.0940712i	−0.837591	+	0.546298i	$0.816037\pi$
$294$		0			0
$295$	1.44289	+	0.833051i	0.0840081	+	0.0485021i
$296$	−5.39270	+	12.6848i	−0.313444	+	0.737287i
$297$		0			0
$298$	8.59810	+	20.9407i	0.498075	+	1.21306i
$299$	2.64491	+	1.52704i	0.152959	+	0.0883109i
$300$		0			0
$301$	21.6814	−	12.5178i	1.24969	−	0.721512i
$302$	−2.04102	−	1.57619i	−0.117448	−	0.0906995i
$303$		0			0
$304$	−10.9257	−	6.48958i	−0.626632	−	0.372203i
$305$			9.42177i			0.539489i
$306$		0			0
$307$	29.0809			1.65973			0.829867	−	0.557961i	$-0.188416\pi$
$307$	29.0809			1.65973			0.829867	+	0.557961i	$0.188416\pi$
$308$	−10.2308	−	39.1495i	−0.582955	−	2.23075i
$309$		0			0
$310$	0.609918	+	0.471012i	0.0346410	+	0.0267517i
$311$	9.36300	+	16.2172i	0.530927	+	0.919593i	0.999349	+	0.0360877i	$0.0114896\pi$
$311$	9.36300	+	16.2172i	0.530927	+	0.919593i	−0.468421	+	0.883505i	$0.655177\pi$
$312$		0			0
$313$	−8.31967	+	14.4101i	−0.470256	+	0.814507i	−0.999421	−	0.0340117i	$-0.989172\pi$
$313$	−8.31967	+	14.4101i	−0.470256	+	0.814507i	0.529166	+	0.848519i	$0.322505\pi$
$314$	−26.8040	+	11.0055i	−1.51264	+	0.621078i
$315$		0			0
$316$	−8.07486	−	8.17543i	−0.454246	−	0.459904i
$317$	−6.55605	+	11.3554i	−0.368224	+	0.637783i	−0.989288	−	0.145977i	$-0.953368\pi$
$317$	−6.55605	+	11.3554i	−0.368224	+	0.637783i	0.621064	+	0.783760i	$0.286701\pi$
$318$		0			0
$319$	−28.8068	+	16.6316i	−1.61287	+	0.931191i
$320$	−2.10224	+	7.30069i	−0.117519	+	0.408121i
$321$		0			0
$322$	0.667973	−	4.95522i	0.0372247	−	0.276144i
$323$			3.78619i			0.210669i
$324$		0			0
$325$			16.6736i			0.924883i
$326$	−10.6429	−	1.43468i	−0.589456	−	0.0794597i
$327$		0			0
$328$	−27.3981	+	3.34858i	−1.51281	+	0.184895i
$329$	40.0565	−	23.1266i	2.20839	−	1.27501i
$330$		0			0
$331$	16.3976	−	28.4014i	0.901292	−	1.56108i	0.0754743	−	0.997148i	$-0.475953\pi$
$331$	16.3976	−	28.4014i	0.901292	−	1.56108i	0.825818	−	0.563937i	$-0.190714\pi$
$332$	−17.5728	−	17.7917i	−0.964433	−	0.976445i
$333$		0			0
$334$	3.01517	+	7.34346i	0.164983	+	0.401816i
$335$	5.20735	−	9.01940i	0.284508	−	0.492782i
$336$		0			0
$337$	−14.1351	−	24.4827i	−0.769986	−	1.33366i	−0.937570	−	0.347798i	$-0.886930\pi$
$337$	−14.1351	−	24.4827i	−0.769986	−	1.33366i	0.167583	−	0.985858i	$-0.446404\pi$
$338$	3.07141	−	3.97720i	0.167063	−	0.216331i
$339$		0			0
$340$	2.19004	−	0.572316i	0.118771	−	0.0310382i
$341$	−2.46475			−0.133474
$342$		0			0
$343$			38.5470i			2.08134i
$344$	12.0119	−	9.04113i	0.647638	−	0.487465i
$345$		0			0
$346$	10.9193	−	14.1395i	0.587026	−	0.760145i
$347$	5.92687	−	3.42188i	0.318171	−	0.183696i	−0.332406	−	0.943136i	$-0.607860\pi$
$347$	5.92687	−	3.42188i	0.318171	−	0.183696i	0.650577	+	0.759440i	$0.274527\pi$
$348$		0			0
$349$	12.5091	+	7.22213i	0.669596	+	0.386592i	0.795924	−	0.605397i	$-0.206986\pi$
$349$	12.5091	+	7.22213i	0.669596	+	0.386592i	−0.126327	+	0.991989i	$0.540319\pi$
$350$	25.2517	−	10.3682i	1.34976	−	0.554203i
$351$		0			0
$352$	−8.95052	−	22.5909i	−0.477065	−	1.20410i
$353$	13.7547	+	7.94128i	0.732088	+	0.422671i	0.819186	−	0.573528i	$-0.194426\pi$
$353$	13.7547	+	7.94128i	0.732088	+	0.422671i	−0.0870973	+	0.996200i	$0.527759\pi$
$354$		0			0
$355$	−4.70582	−	8.15073i	−0.249759	−	0.432596i
$356$	5.37212	−	19.5639i	0.284722	−	1.03689i
$357$		0			0
$358$	−3.87838	+	28.7710i	−0.204979	+	1.52059i
$359$	3.84545			0.202955			0.101477	−	0.994838i	$-0.467643\pi$
$359$	3.84545			0.202955			0.101477	+	0.994838i	$0.467643\pi$
$360$		0			0
$361$	−8.90714			−0.468797
$362$	−1.88186	+	13.9602i	−0.0989083	+	0.733731i
$363$		0			0
$364$	−36.9579	−	10.1484i	−1.93712	−	0.531921i
$365$	4.15452	+	7.19584i	0.217458	+	0.376648i
$366$		0			0
$367$	−23.8803	−	13.7873i	−1.24654	−	0.719692i	−0.276124	−	0.961122i	$-0.589050\pi$
$367$	−23.8803	−	13.7873i	−1.24654	−	0.719692i	−0.970418	+	0.241430i	$0.922384\pi$
$368$	0.0371646	−	3.00237i	0.00193734	−	0.156510i
$369$		0			0
$370$	−6.05438	+	2.48588i	−0.314752	+	0.129235i
$371$	3.58004	+	2.06694i	0.185867	+	0.107310i
$372$		0			0
$373$	7.00779	−	4.04595i	0.362849	−	0.209491i	−0.307481	−	0.951554i	$-0.599486\pi$
$373$	7.00779	−	4.04595i	0.362849	−	0.209491i	0.670330	+	0.742063i	$0.266153\pi$
$374$	−4.42511	+	5.73011i	−0.228817	+	0.296297i
$375$		0			0
$376$	22.1921	−	16.7036i	1.14447	−	0.861420i
$377$			31.5055i			1.62261i
$378$		0			0
$379$	−17.9143			−0.920195			−0.460098	−	0.887868i	$-0.652186\pi$
$379$	−17.9143			−0.920195			−0.460098	+	0.887868i	$0.652186\pi$
$380$	−1.52562	−	5.83799i	−0.0782628	−	0.299482i
$381$		0			0
$382$	−19.8808	+	25.7438i	−1.01719	+	1.31717i
$383$	2.88757	+	5.00142i	0.147548	+	0.255561i	0.930321	−	0.366747i	$-0.119529\pi$
$383$	2.88757	+	5.00142i	0.147548	+	0.255561i	−0.782773	+	0.622308i	$0.786195\pi$
$384$		0			0
$385$	9.60687	−	16.6396i	0.489611	−	0.848032i
$386$	0.537150	+	1.30823i	0.0273402	+	0.0665872i
$387$		0			0
$388$	−11.1419	+	11.0049i	−0.565646	+	0.558688i
$389$	11.0163	−	19.0807i	0.558547	−	0.967432i	−0.439071	−	0.898453i	$-0.644692\pi$
$389$	11.0163	−	19.0807i	0.558547	−	0.967432i	0.997618	−	0.0689799i	$-0.0219744\pi$
$390$		0			0
$391$	−0.774755	+	0.447305i	−0.0391810	+	0.0226212i
$392$	5.21020	+	42.6299i	0.263155	+	2.15313i
$393$		0			0
$394$	0.728294	+	0.0981753i	0.0366909	+	0.00494600i
$395$		−	5.45626i		−	0.274534i
$396$		0			0
$397$			26.3815i			1.32405i	0.749481	+	0.662026i	$0.230303\pi$
$397$			26.3815i			1.32405i	−0.749481	+	0.662026i	$0.769697\pi$
$398$	−0.119148	+	0.883874i	−0.00597234	+	0.0443046i
$399$		0			0
$400$	14.2967	−	8.01993i	0.714836	−	0.400996i
$401$	1.11822	−	0.645607i	0.0558414	−	0.0322401i	−0.471819	−	0.881695i	$-0.656403\pi$
$401$	1.11822	−	0.645607i	0.0558414	−	0.0322401i	0.527661	+	0.849455i	$0.323069\pi$
$402$		0			0
$403$	−1.16725	+	2.02174i	−0.0581451	+	0.100710i
$404$	−25.4039	+	25.0914i	−1.26389	+	1.24834i
$405$		0			0
$406$	47.7144	−	19.5912i	2.36803	−	0.972294i
$407$	10.4666	−	18.1286i	0.518808	−	0.898602i
$408$		0			0
$409$	0.772426	+	1.33788i	0.0381940	+	0.0661539i	0.884490	−	0.466558i	$-0.154506\pi$
$409$	0.772426	+	1.33788i	0.0381940	+	0.0661539i	−0.846297	+	0.532712i	$0.821173\pi$
$410$	−10.3732	−	8.01077i	−0.512297	−	0.395624i
$411$		0			0
$412$	−4.74877	+	1.24098i	−0.233955	+	0.0611388i
$413$	8.26326			0.406608
$414$		0			0
$415$		−	11.8741i		−	0.582878i
$416$	−22.7692	−	3.35678i	−1.11635	−	0.164580i
$417$		0			0
$418$	15.2748	+	11.7960i	0.747113	+	0.576962i
$419$	−12.9309	+	7.46567i	−0.631717	+	0.364722i	−0.781417	−	0.624010i	$-0.785503\pi$
$419$	−12.9309	+	7.46567i	−0.631717	+	0.364722i	0.149700	+	0.988732i	$0.452169\pi$
$420$		0			0
$421$	12.8947	+	7.44478i	0.628451	+	0.362836i	0.780152	−	0.625590i	$-0.215142\pi$
$421$	12.8947	+	7.44478i	0.628451	+	0.362836i	−0.151701	+	0.988426i	$0.548475\pi$
$422$	−5.32742	−	12.9749i	−0.259335	−	0.631611i
$423$		0			0
$424$	2.28458	+	0.971246i	0.110949	+	0.0471679i
$425$	−4.22973	−	2.44204i	−0.205172	−	0.118456i
$426$		0			0
$427$	23.3643	+	40.4681i	1.13068	+	1.95839i
$428$	−0.149983	+	0.546199i	−0.00724968	+	0.0264015i
$429$		0			0
$430$	7.07475	+	0.953690i	0.341175	+	0.0459910i
$431$	30.8436			1.48568			0.742842	−	0.669467i	$-0.233477\pi$
$431$	30.8436			1.48568			0.742842	+	0.669467i	$0.233477\pi$
$432$		0			0
$433$	−29.1892			−1.40275			−0.701373	−	0.712795i	$-0.747429\pi$
$433$	−29.1892			−1.40275			−0.701373	+	0.712795i	$0.747429\pi$
$434$	3.78773	+	0.510593i	0.181817	+	0.0245092i
$435$		0			0
$436$	5.16194	−	18.7985i	0.247212	−	0.900284i
$437$	1.19238	+	2.06527i	0.0570393	+	0.0987950i
$438$		0			0
$439$	1.08226	+	0.624843i	0.0516535	+	0.0298221i	0.525604	−	0.850729i	$-0.323839\pi$
$439$	1.08226	+	0.624843i	0.0516535	+	0.0298221i	−0.473951	+	0.880551i	$0.657173\pi$
$440$	4.51423	−	10.6184i	0.215207	−	0.506213i
$441$		0			0
$442$	2.60456	+	6.34340i	0.123886	+	0.301725i
$443$	23.7521	+	13.7133i	1.12850	+	0.651538i	0.943556	−	0.331212i	$-0.107458\pi$
$443$	23.7521	+	13.7133i	1.12850	+	0.651538i	0.184940	+	0.982750i	$0.440791\pi$
$444$		0			0
$445$	8.34282	−	4.81673i	0.395487	−	0.228335i
$446$	7.95517	+	6.14342i	0.376688	+	0.290900i
$447$		0			0
$448$	9.07490	+	36.5709i	0.428749	+	1.72781i
$449$		−	16.2552i		−	0.767132i	−0.923513	−	0.383566i	$-0.874696\pi$
$449$		−	16.2552i		−	0.767132i	0.923513	−	0.383566i	$-0.125304\pi$
$450$		0			0
$451$	41.9194			1.97391
$452$	−9.14749	+	2.39049i	−0.430262	+	0.112439i
$453$		0			0
$454$	13.9488	+	10.7721i	0.654652	+	0.505558i
$455$	−9.09921	−	15.7603i	−0.426578	−	0.738854i
$456$		0			0
$457$	−9.44307	+	16.3559i	−0.441728	+	0.765096i	−0.997818	−	0.0660267i	$-0.978968\pi$
$457$	−9.44307	+	16.3559i	−0.441728	+	0.765096i	0.556090	+	0.831122i	$0.312301\pi$
$458$	12.7798	−	5.24727i	0.597159	−	0.245189i
$459$		0			0
$460$	1.01437	−	1.00189i	0.0472951	−	0.0467133i
$461$	−9.65240	+	16.7184i	−0.449557	+	0.778655i	−0.998357	−	0.0572981i	$-0.981751\pi$
$461$	−9.65240	+	16.7184i	−0.449557	+	0.778655i	0.548800	+	0.835954i	$0.315085\pi$
$462$		0			0
$463$	2.02823	−	1.17100i	0.0942598	−	0.0544209i	−0.452129	−	0.891952i	$-0.649335\pi$
$463$	2.02823	−	1.17100i	0.0942598	−	0.0544209i	0.546389	+	0.837532i	$0.316002\pi$
$464$	27.0143	−	15.1540i	1.25411	−	0.703508i
$465$		0			0
$466$	0.881146	−	6.53660i	0.0408183	−	0.302802i
$467$			12.2034i			0.564708i	0.959310	+	0.282354i	$0.0911153\pi$
$467$			12.2034i			0.564708i	−0.959310	+	0.282354i	$0.908885\pi$
$468$		0			0
$469$		−	51.6531i		−	2.38512i
$470$	13.0707	+	1.76195i	0.602904	+	0.0812726i
$471$		0			0
$472$	4.92556	−	0.602000i	0.226717	−	0.0277093i
$473$	−19.7736	+	11.4163i	−0.909193	+	0.524923i
$474$		0			0
$475$	−6.50974	+	11.2752i	−0.298687	+	0.517341i
$476$	7.98735	−	7.88909i	0.366100	−	0.361596i
$477$		0			0
$478$	1.83991	+	4.48111i	0.0841555	+	0.204961i
$479$	−17.7237	+	30.6983i	−0.809815	+	1.40264i	0.103177	+	0.994663i	$0.467099\pi$
$479$	−17.7237	+	30.6983i	−0.809815	+	1.40264i	−0.912992	+	0.407978i	$0.866234\pi$
$480$		0			0
$481$	−9.91348	−	17.1706i	−0.452016	−	0.782914i
$482$	−1.08543	+	1.40553i	−0.0494398	+	0.0640201i
$483$		0			0
$484$	3.76820	+	14.4195i	0.171282	+	0.655432i
$485$	−7.43610			−0.337656
$486$		0			0
$487$		−	18.7853i		−	0.851242i	−0.904902	−	0.425621i	$-0.860056\pi$
$487$		−	18.7853i		−	0.851242i	0.904902	−	0.425621i	$-0.139944\pi$
$488$	16.8752	+	22.4201i	0.763904	+	1.01491i
$489$		0			0
$490$	−12.4643	+	16.1401i	−0.563079	+	0.729136i
$491$	1.06466	−	0.614681i	0.0480474	−	0.0277402i	−0.475784	−	0.879562i	$-0.657836\pi$
$491$	1.06466	−	0.614681i	0.0480474	−	0.0277402i	0.523831	+	0.851822i	$0.324502\pi$
$492$		0			0
$493$	−7.99227	−	4.61434i	−0.359954	−	0.207819i
$494$	16.9096	−	6.94297i	0.760800	−	0.312379i
$495$		0			0
$496$	2.29499	+	0.0284082i	0.103048	+	0.00127557i
$497$	−40.4246	−	23.3392i	−1.81329	−	1.04690i
$498$		0			0
$499$	1.73661	+	3.00789i	0.0777413	+	0.134652i	0.902275	−	0.431161i	$-0.141896\pi$
$499$	1.73661	+	3.00789i	0.0777413	+	0.134652i	−0.824534	+	0.565813i	$0.808563\pi$
$500$	16.6636	+	4.57571i	0.745217	+	0.204632i
$501$		0			0
$502$	3.82280	−	28.3587i	0.170620	−	1.26571i
$503$	31.5709			1.40768			0.703838	−	0.710360i	$-0.251468\pi$
$503$	31.5709			1.40768			0.703838	+	0.710360i	$0.251468\pi$
$504$		0			0
$505$	−16.9545			−0.754465
$506$	−0.609198	+	4.51921i	−0.0270822	+	0.200903i
$507$		0			0
$508$	7.31048	−	26.6229i	0.324350	−	1.18120i
$509$	15.7887	+	27.3468i	0.699820	+	1.21212i	0.968529	+	0.248902i	$0.0800698\pi$
$509$	15.7887	+	27.3468i	0.699820	+	1.21212i	−0.268709	+	0.963222i	$0.586597\pi$
$510$		0			0
$511$	35.6888	+	20.6049i	1.57878	+	0.911508i
$512$	8.07365	+	21.1380i	0.356808	+	0.934178i
$513$		0			0
$514$	1.53866	−	0.631764i	0.0678675	−	0.0278659i
$515$	−2.01836	−	1.16530i	−0.0889394	−	0.0513492i
$516$		0			0
$517$	−36.5319	+	21.0917i	−1.60667	+	0.927613i
$518$	−19.8400	+	25.6910i	−0.871721	+	1.12880i
$519$		0			0
$520$	−6.57204	−	8.73150i	−0.288203	−	0.382901i
$521$			8.99232i			0.393961i	0.980407	+	0.196980i	$0.0631136\pi$
$521$			8.99232i			0.393961i	−0.980407	+	0.196980i	$0.936886\pi$
$522$		0			0
$523$	2.78978			0.121988			0.0609942	−	0.998138i	$-0.480573\pi$
$523$	2.78978			0.121988			0.0609942	+	0.998138i	$0.480573\pi$
$524$	−9.16159	+	2.39417i	−0.400226	+	0.104590i
$525$		0			0
$526$	−6.07174	+	7.86235i	−0.264740	+	0.342815i
$527$	−0.341916	−	0.592215i	−0.0148941	−	0.0257973i
$528$		0			0
$529$	11.2183	−	19.4306i	0.487751	−	0.844809i
$530$	0.447717	+	1.09042i	0.0194476	+	0.0473647i
$531$		0			0
$532$	−21.0300	−	21.2919i	−0.911764	−	0.923120i
$533$	19.8521	−	34.3849i	0.859892	−	1.48938i
$534$		0			0
$535$	−0.232920	+	0.134477i	−0.0100700	+	0.00581393i
$536$	−3.76307	−	30.7894i	−0.162540	−	1.32990i
$537$		0			0
$538$	−16.0016	−	2.15705i	−0.689879	−	0.0929970i
$539$		−	65.2242i		−	2.80940i
$540$		0			0
$541$		−	38.5456i		−	1.65721i	−0.559836	−	0.828603i	$-0.689136\pi$
$541$		−	38.5456i		−	1.65721i	0.559836	−	0.828603i	$-0.310864\pi$
$542$	−2.07643	+	15.4036i	−0.0891904	+	0.661641i
$543$		0			0
$544$	4.18636	−	5.28443i	0.179489	−	0.226568i
$545$	8.01641	−	4.62828i	0.343385	−	0.198254i
$546$		0			0
$547$	−10.8890	+	18.8604i	−0.465581	+	0.806411i	−0.999228	−	0.0392972i	$-0.987488\pi$
$547$	−10.8890	+	18.8604i	−0.465581	+	0.806411i	0.533646	+	0.845708i	$0.320821\pi$
$548$	21.8606	+	22.1329i	0.933838	+	0.945469i
$549$		0			0
$550$	−23.0298	+	9.45589i	−0.981996	+	0.403200i
$551$	−12.3005	+	21.3050i	−0.524017	+	0.907624i
$552$		0			0
$553$	−13.5305	−	23.4356i	−0.575377	−	0.996582i
$554$	4.03139	+	3.11326i	0.171278	+	0.132270i
$555$		0			0
$556$	−3.98965	−	15.2669i	−0.169199	−	0.647461i
$557$	−22.9871			−0.973995			−0.486998	−	0.873403i	$-0.661908\pi$
$557$	−22.9871			−0.973995			−0.486998	+	0.873403i	$0.661908\pi$
$558$		0			0
$559$			21.6261i			0.914686i
$560$	−9.13695	+	15.3828i	−0.386107	+	0.650040i
$561$		0			0
$562$	−13.7384	−	10.6095i	−0.579518	−	0.447536i
$563$	−35.7358	+	20.6321i	−1.50608	+	0.869537i	−0.506108	+	0.862470i	$0.668916\pi$
$563$	−35.7358	+	20.6321i	−1.50608	+	0.869537i	−0.999975	+	0.00706728i	$0.997750\pi$
$564$		0			0
$565$	−3.88793	−	2.24470i	−0.163567	−	0.0944352i
$566$	1.36691	+	3.32910i	0.0574553	+	0.139933i
$567$		0			0
$568$	−25.7966	−	10.9670i	−1.08240	−	0.460164i
$569$	−24.6609	−	14.2380i	−1.03384	−	0.596888i	−0.115757	−	0.993278i	$-0.536930\pi$
$569$	−24.6609	−	14.2380i	−1.03384	−	0.596888i	−0.918082	+	0.396390i	$0.870263\pi$
$570$		0			0
$571$	17.7603	+	30.7617i	0.743245	+	1.28734i	0.951010	+	0.309159i	$0.100048\pi$
$571$	17.7603	+	30.7617i	0.743245	+	1.28734i	−0.207765	+	0.978179i	$0.566619\pi$
$572$	33.7060	+	9.25544i	1.40932	+	0.386990i
$573$		0			0
$574$	−64.4200	−	8.68393i	−2.68884	−	0.362460i
$575$	−3.07627			−0.128289
$576$		0			0
$577$	−30.5676			−1.27255			−0.636273	−	0.771464i	$-0.719525\pi$
$577$	−30.5676			−1.27255			−0.636273	+	0.771464i	$0.719525\pi$
$578$	21.8355	+	2.94346i	0.908236	+	0.122432i
$579$		0			0
$580$	14.1827	+	3.89448i	0.588906	+	0.161710i
$581$	−29.4457	−	51.0014i	−1.22161	−	2.11589i
$582$		0			0
$583$	−3.26504	−	1.88507i	−0.135224	−	0.0780716i
$584$	22.7745	+	9.68216i	0.942415	+	0.400651i
$585$		0			0
$586$	0.998748	+	2.43245i	0.0412579	+	0.100484i
$587$	−16.1608	−	9.33044i	−0.667028	−	0.385109i	0.127922	−	0.991784i	$-0.459169\pi$
$587$	−16.1608	−	9.33044i	−0.667028	−	0.385109i	−0.794949	+	0.606676i	$0.792503\pi$
$588$		0			0
$589$	−1.57867	+	0.911445i	−0.0650479	+	0.0375554i
$590$	1.86487	+	1.44016i	0.0767755	+	0.0592903i
$591$		0			0
$592$	−9.95459	+	16.7593i	−0.409131	+	0.688804i
$593$			0.676531i			0.0277818i	0.999904	+	0.0138909i	$0.00442175\pi$
$593$			0.676531i			0.0277818i	−0.999904	+	0.0138909i	$0.995578\pi$
$594$		0			0
$595$	5.33074			0.218539
$596$	8.09423	+	30.9736i	0.331553	+	1.26873i
$597$		0			0
$598$	3.41843	+	2.63990i	0.139790	+	0.107954i
$599$	−18.8685	−	32.6813i	−0.770947	−	1.33532i	−0.937044	−	0.349211i	$-0.886450\pi$
$599$	−18.8685	−	32.6813i	−0.770947	−	1.33532i	0.166097	−	0.986109i	$-0.446884\pi$
$600$		0			0
$601$	11.5562	−	20.0159i	0.471386	−	0.816464i	−0.528078	−	0.849196i	$-0.677087\pi$
$601$	11.5562	−	20.0159i	0.471386	−	0.816464i	0.999464	+	0.0327315i	$0.0104206\pi$
$602$	32.7523	−	13.4478i	1.33488	−	0.548093i
$603$		0			0
$604$	−2.56278	−	2.59470i	−0.104278	−	0.105577i
$605$	−3.53839	+	6.12868i	−0.143856	+	0.249166i
$606$		0			0
$607$	2.04207	−	1.17899i	0.0828851	−	0.0478537i	−0.457985	−	0.888960i	$-0.651429\pi$
$607$	2.04207	−	1.17899i	0.0828851	−	0.0478537i	0.540870	+	0.841106i	$0.318095\pi$
$608$	−14.0867	−	11.1596i	−0.571291	−	0.452581i
$609$		0			0
$610$	−1.78005	+	13.2050i	−0.0720723	+	0.534653i
$611$			39.9543i			1.61638i
$612$		0			0
$613$		−	23.7808i		−	0.960497i	−0.877132	−	0.480249i	$-0.840546\pi$
$613$		−	23.7808i		−	0.960497i	0.877132	−	0.480249i	$-0.159454\pi$
$614$	40.7580	+	5.49425i	1.64486	+	0.221730i
$615$		0			0
$616$	−6.94236	−	56.8023i	−0.279715	−	2.28863i
$617$	−3.17492	+	1.83304i	−0.127817	+	0.0737954i	−0.562545	−	0.826766i	$-0.690178\pi$
$617$	−3.17492	+	1.83304i	−0.127817	+	0.0737954i	0.434728	+	0.900562i	$0.356845\pi$
$618$		0			0
$619$	8.79359	−	15.2309i	0.353444	−	0.612183i	−0.633406	−	0.773820i	$-0.718344\pi$
$619$	8.79359	−	15.2309i	0.353444	−	0.612183i	0.986850	+	0.161636i	$0.0516771\pi$
$620$	0.765834	+	0.775373i	0.0307566	+	0.0311397i
$621$		0			0
$622$	10.0587	+	24.4979i	0.403316	+	0.982278i
$623$	23.8892	−	41.3773i	0.957101	−	1.65775i
$624$		0			0
$625$	−6.14269	−	10.6394i	−0.245708	−	0.425578i
$626$	−14.3828	+	18.6244i	−0.574853	+	0.744383i
$627$		0			0
$628$	−39.6460	+	10.3606i	−1.58205	+	0.413432i
$629$	5.80777			0.231571
$630$		0			0
$631$		−	21.9248i		−	0.872811i	−0.899750	−	0.436405i	$-0.856251\pi$
$631$		−	21.9248i		−	0.872811i	0.899750	−	0.436405i	$-0.143749\pi$
$632$	−9.77263	−	12.9837i	−0.388734	−	0.516466i
$633$		0			0
$634$	−11.3339	+	14.6764i	−0.450127	+	0.582874i
$635$	11.3530	−	6.55468i	0.450532	−	0.260115i
$636$		0			0
$637$	−53.5009	−	30.8888i	−2.11978	−	1.22386i
$638$	−43.5160	+	17.8674i	−1.72281	+	0.707375i
$639$		0			0
$640$	−4.32568	+	9.83500i	−0.170988	+	0.388763i
$641$	18.0562	+	10.4248i	0.713178	+	0.411754i	0.812237	−	0.583328i	$-0.198250\pi$
$641$	18.0562	+	10.4248i	0.713178	+	0.411754i	−0.0990584	+	0.995082i	$0.531583\pi$
$642$		0			0
$643$	12.8540	+	22.2638i	0.506914	+	0.878000i	0.999968	+	0.00800162i	$0.00254702\pi$
$643$	12.8540	+	22.2638i	0.506914	+	0.878000i	−0.493054	+	0.869998i	$0.664120\pi$
$644$	1.87238	−	6.81873i	0.0737820	−	0.268696i
$645$		0			0
$646$	−0.715325	+	5.30649i	−0.0281441	+	0.208781i
$647$	−26.0025			−1.02226			−0.511131	−	0.859503i	$-0.670773\pi$
$647$	−26.0025			−1.02226			−0.511131	+	0.859503i	$0.670773\pi$
$648$		0			0
$649$	−7.53617			−0.295821
$650$	−3.15013	+	23.3686i	−0.123558	+	0.916592i
$651$		0			0
$652$	−14.6454	−	4.02152i	−0.573557	−	0.157495i
$653$	10.7670	+	18.6490i	0.421346	+	0.729792i	0.996071	−	0.0885542i	$-0.0282246\pi$
$653$	10.7670	+	18.6490i	0.421346	+	0.729792i	−0.574726	+	0.818346i	$0.694891\pi$
$654$		0			0
$655$	−3.89392	−	2.24816i	−0.152148	−	0.0878428i
$656$	−39.0321	−	0.483155i	−1.52395	−	0.0188640i
$657$		0			0
$658$	60.5100	−	24.8450i	2.35893	−	0.968558i
$659$	11.5947	+	6.69419i	0.451665	+	0.260769i	0.708533	−	0.705678i	$-0.249357\pi$
$659$	11.5947	+	6.69419i	0.451665	+	0.260769i	−0.256868	+	0.966446i	$0.582691\pi$
$660$		0			0
$661$	14.4644	−	8.35103i	0.562600	−	0.324818i	−0.191588	−	0.981475i	$-0.561364\pi$
$661$	14.4644	−	8.35103i	0.562600	−	0.324818i	0.754189	+	0.656658i	$0.228030\pi$
$662$	28.3477	−	36.7077i	1.10176	−	1.42668i
$663$		0			0
$664$	−21.2676	−	28.2557i	−0.825341	−	1.09653i
$665$		−	14.2102i		−	0.551046i
$666$		0			0
$667$	−5.81275			−0.225071
$668$	2.83848	+	10.8618i	0.109824	+	0.420255i
$669$		0			0
$670$	9.00233	−	11.6572i	0.347790	−	0.450357i
$671$	−21.3085	−	36.9073i	−0.822604	−	1.42479i
$672$		0			0
$673$	−5.47889	+	9.48971i	−0.211196	+	0.365802i	−0.952089	−	0.305821i	$-0.901069\pi$
$673$	−5.47889	+	9.48971i	−0.211196	+	0.365802i	0.740893	+	0.671623i	$0.234402\pi$
$674$	−15.1853	−	36.9839i	−0.584917	−	1.42457i
$675$		0			0
$676$	5.05610	−	4.99391i	0.194466	−	0.192073i
$677$	11.2742	−	19.5275i	0.433302	−	0.750501i	−0.563853	−	0.825875i	$-0.690682\pi$
$677$	11.2742	−	19.5275i	0.433302	−	0.750501i	0.997155	+	0.0753738i	$0.0240150\pi$
$678$		0			0
$679$	−31.9393	+	18.4402i	−1.22572	+	0.707669i
$680$	3.17755	−	0.388358i	0.121853	−	0.0148929i
$681$		0			0
$682$	−3.45444	−	0.465665i	−0.132277	−	0.0178313i
$683$		−	36.4666i		−	1.39536i	−0.716412	−	0.697678i	$-0.754217\pi$
$683$		−	36.4666i		−	1.39536i	0.716412	−	0.697678i	$-0.245783\pi$
$684$		0			0
$685$			14.7714i			0.564387i
$686$	−7.28268	+	54.0250i	−0.278054	+	2.06269i
$687$		0			0
$688$	18.5433	−	10.4021i	0.706955	−	0.396575i
$689$	−3.09250	+	1.78546i	−0.117815	+	0.0680205i
$690$		0			0
$691$	−2.50258	+	4.33459i	−0.0952025	+	0.164896i	−0.909693	−	0.415281i	$-0.863683\pi$
$691$	−2.50258	+	4.33459i	−0.0952025	+	0.164896i	0.814491	+	0.580177i	$0.197017\pi$
$692$	17.9752	−	17.7541i	0.683315	−	0.674909i
$693$		0			0
$694$	8.95322	−	3.67613i	0.339860	−	0.139544i
$695$	3.74634	−	6.48884i	0.142107	−	0.246136i
$696$		0			0
$697$	5.81515	+	10.0721i	0.220265	+	0.381509i
$698$	16.1675	+	12.4854i	0.611948	+	0.472580i
$699$		0			0
$700$	37.3501	−	9.76059i	1.41170	−	0.368916i
$701$	11.4972			0.434243			0.217122	−	0.976145i	$-0.430333\pi$
$701$	11.4972			0.434243			0.217122	+	0.976145i	$0.430333\pi$
$702$		0			0
$703$		−	15.4818i		−	0.583907i
$704$	−8.27640	−	33.3530i	−0.311929	−	1.25704i
$705$		0			0
$706$	17.7774	+	13.7287i	0.669060	+	0.516685i
$707$	−72.8225	+	42.0441i	−2.73877	+	1.58123i
$708$		0			0
$709$	29.7367	+	17.1685i	1.11679	+	0.644776i	0.940578	−	0.339577i	$-0.110284\pi$
$709$	29.7367	+	17.1685i	1.11679	+	0.644776i	0.176207	+	0.984353i	$0.443617\pi$
$710$	−5.05547	−	12.3126i	−0.189728	−	0.462084i
$711$		0			0
$712$	11.2254	−	26.4046i	0.420691	−	0.989554i
$713$	−0.373011	−	0.215358i	−0.0139694	−	0.00806523i
$714$		0			0
$715$	8.29857	+	14.3735i	0.310349	+	0.537540i
$716$	−10.8714	+	39.5909i	−0.406283	+	1.47958i
$717$		0			0
$718$	5.38954	+	0.726519i	0.201136	+	0.0271135i
$719$	40.5660			1.51286			0.756429	−	0.654076i	$-0.226942\pi$
$719$	40.5660			1.51286			0.756429	+	0.654076i	$0.226942\pi$
$720$		0			0
$721$	−11.5589			−0.430477
$722$	−12.4837	−	1.68282i	−0.464594	−	0.0626282i
$723$		0			0
$724$	−5.27499	+	19.2102i	−0.196043	+	0.713940i
$725$	−15.8672	−	27.4828i	−0.589293	−	1.02069i
$726$		0			0
$727$	−33.7590	−	19.4908i	−1.25205	−	0.722873i	−0.280535	−	0.959844i	$-0.590512\pi$
$727$	−33.7590	−	19.4908i	−1.25205	−	0.722873i	−0.971517	+	0.236971i	$0.923845\pi$
$728$	−49.8805	−	21.2058i	−1.84870	−	0.785940i
$729$		0			0
$730$	4.46321	+	10.8701i	0.165191	+	0.402322i
$731$	−5.48608	−	3.16739i	−0.202910	−	0.117150i
$732$		0			0
$733$	31.5208	−	18.1986i	1.16425	−	0.672179i	0.211930	−	0.977285i	$-0.432025\pi$
$733$	31.5208	−	18.1986i	1.16425	−	0.672179i	0.952319	+	0.305105i	$0.0986917\pi$
$734$	−30.8643	−	23.8351i	−1.13922	−	0.879771i
$735$		0			0
$736$	0.619325	−	4.20092i	0.0228286	−	0.154848i
$737$			47.1082i			1.73525i
$738$		0			0
$739$	−19.8657			−0.730770			−0.365385	−	0.930857i	$-0.619063\pi$
$739$	−19.8657			−0.730770			−0.365385	+	0.930857i	$0.619063\pi$
$740$	−8.95509	+	2.34021i	−0.329196	+	0.0860276i
$741$		0			0
$742$	4.62706	+	3.57327i	0.169865	+	0.131179i
$743$	6.13689	+	10.6294i	0.225141	+	0.389955i	0.956362	−	0.292186i	$-0.0943825\pi$
$743$	6.13689	+	10.6294i	0.225141	+	0.389955i	−0.731221	+	0.682141i	$0.761049\pi$
$744$		0			0
$745$	−7.60060	+	13.1646i	−0.278464	+	0.482314i
$746$	10.5861	−	4.34657i	0.387584	−	0.159139i
$747$		0			0
$748$	−7.28454	+	7.19493i	−0.266349	+	0.263073i
$749$	−0.666955	+	1.15520i	−0.0243700	+	0.0422101i
$750$		0			0
$751$	4.29326	−	2.47872i	0.156663	−	0.0904496i	−0.419619	−	0.907700i	$-0.637836\pi$
$751$	4.29326	−	2.47872i	0.156663	−	0.0904496i	0.576282	+	0.817251i	$0.304503\pi$
$752$	34.2588	−	19.2179i	1.24929	−	0.700805i
$753$		0			0
$754$	−5.95232	+	44.1561i	−0.216771	+	1.60807i
$755$		−	1.73169i		−	0.0630228i
$756$		0			0
$757$		−	0.135856i		−	0.00493778i	−0.999997	−	0.00246889i	$-0.999214\pi$
$757$		−	0.135856i		−	0.00493778i	0.999997	−	0.00246889i	$-0.000785872\pi$
$758$	−25.1075	−	3.38454i	−0.911947	−	0.122932i
$759$		0			0
$760$	−1.03525	−	8.47039i	−0.0375524	−	0.307253i
$761$	−1.85960	+	1.07364i	−0.0674106	+	0.0389195i	−0.533326	−	0.845910i	$-0.679058\pi$
$761$	−1.85960	+	1.07364i	−0.0674106	+	0.0389195i	0.465916	+	0.884829i	$0.345725\pi$
$762$		0			0
$763$	22.9546	−	39.7585i	0.831011	−	1.43935i
$764$	−32.7274	+	32.3248i	−1.18403	+	1.16947i
$765$		0			0
$766$	3.10212	+	7.55523i	0.112084	+	0.272981i
$767$	−3.56897	+	6.18164i	−0.128868	+	0.223206i
$768$		0			0
$769$	6.85585	+	11.8747i	0.247228	+	0.428212i	0.962756	−	0.270373i	$-0.0871469\pi$
$769$	6.85585	+	11.8747i	0.247228	+	0.428212i	−0.715527	+	0.698585i	$0.753814\pi$
$770$	16.6081	−	21.5060i	0.598514	−	0.775021i
$771$		0			0
$772$	0.505672	+	1.93502i	0.0181995	+	0.0696428i
$773$	21.2269			0.763477			0.381738	−	0.924270i	$-0.375326\pi$
$773$	21.2269			0.763477			0.381738	+	0.924270i	$0.375326\pi$
$774$		0			0
$775$		−	2.35147i		−	0.0844673i
$776$	−17.6950	+	13.3187i	−0.635213	+	0.478113i
$777$		0			0
$778$	19.0446	−	24.6611i	0.682783	−	0.884142i
$779$	26.8493	−	15.5015i	0.961976	−	0.555397i
$780$		0			0
$781$	36.8677	+	21.2856i	1.31923	+	0.761657i
$782$	−1.17036	+	0.480540i	−0.0418519	+	0.0171841i
$783$		0			0
$784$	−0.751761	+	60.7317i	−0.0268486	+	2.16899i
$785$	−16.8506	−	9.72872i	−0.601425	−	0.347233i
$786$		0			0
$787$	−10.6033	−	18.3654i	−0.377966	−	0.654657i	0.612800	−	0.790238i	$-0.290043\pi$
$787$	−10.6033	−	18.3654i	−0.377966	−	0.654657i	−0.990766	+	0.135581i	$0.956710\pi$
$788$	1.00218	+	0.275193i	0.0357013	+	0.00980333i
$789$		0			0
$790$	1.03085	−	7.64715i	0.0366760	−	0.272073i
$791$	−22.2658			−0.791680
$792$		0			0
$793$	−40.3649			−1.43340
$794$	−4.98426	+	36.9747i	−0.176885	+	1.31218i
$795$		0			0
$796$	−0.333980	+	1.21627i	−0.0118376	+	0.0431096i
$797$	−17.6435	−	30.5595i	−0.624967	−	1.08247i	−0.988547	−	0.150911i	$-0.951779\pi$
$797$	−17.6435	−	30.5595i	−0.624967	−	1.08247i	0.363581	−	0.931563i	$-0.381554\pi$
$798$		0			0
$799$	−10.1356	−	5.85178i	−0.358571	−	0.207021i
$800$	21.5526	−	8.53915i	0.761999	−	0.301904i
$801$		0			0
$802$	1.68921	−	0.693576i	0.0596479	−	0.0244910i
$803$	−32.5485	−	18.7919i	−1.14861	−	0.663151i
$804$		0			0
$805$	2.90777	−	1.67880i	0.102485	−	0.0591700i
$806$	−2.01792	+	2.61302i	−0.0710781	+	0.0920397i
$807$		0			0
$808$	−40.3450	+	30.3669i	−1.41933	+	1.06831i
$809$			26.8216i			0.942996i	0.881867	+	0.471498i	$0.156286\pi$
$809$			26.8216i			0.942996i	−0.881867	+	0.471498i	$0.843714\pi$
$810$		0			0
$811$	7.68860			0.269983			0.134992	−	0.990847i	$-0.456899\pi$
$811$	7.68860			0.269983			0.134992	+	0.990847i	$0.456899\pi$
$812$	70.5748	−	18.4431i	2.47669	−	0.647226i
$813$		0			0
$814$	18.0943	−	23.4305i	0.634205	−	0.821238i
$815$	−3.60576	−	6.24535i	−0.126304	−	0.218765i
$816$		0			0
$817$	−8.44332	+	14.6243i	−0.295394	+	0.511638i
$818$	0.829818	+	2.02102i	0.0290139	+	0.0706634i
$819$		0			0
$820$	−13.0250	−	13.1872i	−0.454852	−	0.460517i
$821$	12.3690	−	21.4237i	0.431680	−	0.747692i	−0.565338	−	0.824859i	$-0.691254\pi$
$821$	12.3690	−	21.4237i	0.431680	−	0.747692i	0.997018	+	0.0771675i	$0.0245876\pi$
$822$		0			0
$823$	−27.2907	+	15.7563i	−0.951294	+	0.549230i	−0.893483	−	0.449098i	$-0.851745\pi$
$823$	−27.2907	+	15.7563i	−0.951294	+	0.549230i	−0.0578112	+	0.998328i	$0.518412\pi$
$824$	−6.89004	+	0.842097i	−0.240026	+	0.0293359i
$825$		0			0
$826$	11.5813	+	1.56118i	0.402964	+	0.0543203i
$827$			15.9087i			0.553200i	0.960985	+	0.276600i	$0.0892077\pi$
$827$			15.9087i			0.553200i	−0.960985	+	0.276600i	$0.910792\pi$
$828$		0			0
$829$			40.2678i			1.39856i	0.714848	+	0.699280i	$0.246496\pi$
$829$			40.2678i			1.39856i	−0.714848	+	0.699280i	$0.753504\pi$
$830$	2.24337	−	16.6420i	0.0778687	−	0.577653i
$831$		0			0
$832$	−31.2777	−	9.00643i	−1.08436	−	0.312242i
$833$	15.6717	−	9.04803i	0.542991	−	0.313496i
$834$		0			0
$835$	−2.66537	+	4.61655i	−0.0922389	+	0.159762i
$836$	19.1795	+	19.4184i	0.663338	+	0.671600i
$837$		0			0
$838$	−19.5337	+	8.02038i	−0.674779	+	0.277059i
$839$	−2.66890	+	4.62267i	−0.0921408	+	0.159592i	−0.908412	−	0.418077i	$-0.862704\pi$
$839$	−2.66890	+	4.62267i	−0.0921408	+	0.159592i	0.816271	+	0.577669i	$0.196038\pi$
$840$		0			0
$841$	−15.4818	−	26.8153i	−0.533856	−	0.924666i
$842$	16.6659	+	12.8703i	0.574345	+	0.443541i
$843$		0			0
$844$	−5.01522	−	19.1914i	−0.172631	−	0.660594i
$845$	3.37443			0.116084
$846$		0			0
$847$			35.0983i			1.20599i
$848$	3.01842	+	1.79286i	0.103653	+	0.0615671i
$849$		0			0
$850$	−5.46675	−	4.22172i	−0.187508	−	0.144804i
$851$	3.16798	−	1.82903i	0.108597	−	0.0626985i
$852$		0			0
$853$	28.1392	+	16.2462i	0.963468	+	0.556258i	0.897239	−	0.441546i	$-0.145570\pi$
$853$	28.1392	+	16.2462i	0.963468	+	0.556258i	0.0662290	+	0.997804i	$0.478903\pi$
$854$	25.1003	+	61.1318i	0.858913	+	2.09189i
$855$		0			0
$856$	−0.313399	+	0.737181i	−0.0107118	+	0.0251963i
$857$	−21.1136	−	12.1899i	−0.721227	−	0.416400i	0.0939774	−	0.995574i	$-0.470042\pi$
$857$	−21.1136	−	12.1899i	−0.721227	−	0.416400i	−0.815204	+	0.579174i	$0.803375\pi$
$858$		0			0
$859$	6.04812	+	10.4757i	0.206359	+	0.357425i	0.950565	−	0.310526i	$-0.100505\pi$
$859$	6.04812	+	10.4757i	0.206359	+	0.357425i	−0.744206	+	0.667951i	$0.767172\pi$
$860$	9.73535	+	2.67326i	0.331973	+	0.0911575i
$861$		0			0
$862$	43.2284	+	5.82728i	1.47237	+	0.198478i
$863$	−39.4505			−1.34291			−0.671456	−	0.741044i	$-0.734331\pi$
$863$	−39.4505			−1.34291			−0.671456	+	0.741044i	$0.734331\pi$
$864$		0			0
$865$	11.9966			0.407897
$866$	−40.9098	−	5.51472i	−1.39017	−	0.187398i
$867$		0			0
$868$	5.21217	+	1.43123i	0.176913	+	0.0485791i
$869$	12.3400	+	21.3735i	0.418605	+	0.725046i
$870$		0			0
$871$	38.6410	+	22.3094i	1.30930	+	0.755925i
$872$	10.7862	−	25.3715i	0.365268	−	0.859188i
$873$		0			0
$874$	1.28098	+	3.11982i	0.0433297	+	0.105530i
$875$	35.2431	+	20.3476i	1.19144	+	0.687876i
$876$		0			0
$877$	5.96635	−	3.44467i	0.201469	−	0.116318i	−0.395871	−	0.918306i	$-0.629557\pi$
$877$	5.96635	−	3.44467i	0.201469	−	0.116318i	0.597341	+	0.801988i	$0.296224\pi$
$878$	1.39878	+	1.08021i	0.0472064	+	0.0364554i
$879$		0			0
$880$	8.33299	−	14.0292i	0.280905	−	0.472925i
$881$		−	44.3192i		−	1.49315i	−0.665300	−	0.746576i	$-0.731696\pi$
$881$		−	44.3192i		−	1.49315i	0.665300	−	0.746576i	$-0.268304\pi$
$882$		0			0
$883$	48.0579			1.61728			0.808639	−	0.588305i	$-0.200205\pi$
$883$	48.0579			1.61728			0.808639	+	0.588305i	$0.200205\pi$
$884$	2.45192	+	9.38259i	0.0824671	+	0.315571i
$885$		0			0
$886$	30.6986	+	23.7072i	1.03134	+	0.796457i
$887$	13.5146	+	23.4079i	0.453775	+	0.785961i	0.998617	−	0.0525774i	$-0.0167436\pi$
$887$	13.5146	+	23.4079i	0.453775	+	0.785961i	−0.544842	+	0.838539i	$0.683410\pi$
$888$		0			0
$889$	32.5088	−	56.3070i	1.09031	−	1.88848i
$890$	12.6028	−	5.17461i	0.422446	−	0.173453i
$891$		0			0
$892$	9.98879	+	10.1132i	0.334450	+	0.338615i
$893$	−15.5991	+	27.0184i	−0.522004	+	0.904137i
$894$		0			0
$895$	−16.8831	+	9.74746i	−0.564340	+	0.325822i
$896$	5.80949	+	52.9699i	0.194081	+	1.76960i
$897$		0			0
$898$	3.07110	−	22.7823i	0.102484	−	0.760256i
$899$		−	4.44322i		−	0.148190i
$900$		0			0
$901$		−	1.04600i		−	0.0348474i
$902$	58.7516	+	7.91983i	1.95622	+	0.263702i
$903$		0			0
$904$	−13.2722	+	1.62212i	−0.441426	+	0.0539509i
$905$	−8.19196	+	4.72963i	−0.272310	+	0.157218i
$906$		0			0
$907$	−2.71996	+	4.71111i	−0.0903149	+	0.156430i	−0.907644	−	0.419742i	$-0.862121\pi$
$907$	−2.71996	+	4.71111i	−0.0903149	+	0.156430i	0.817329	+	0.576172i	$0.195454\pi$
$908$	17.5147	+	17.7328i	0.581244	+	0.588484i
$909$		0			0
$910$	−9.77529	−	23.8077i	−0.324048	−	0.789219i
$911$	19.7758	−	34.2528i	0.655203	−	1.13484i	−0.326640	−	0.945149i	$-0.605917\pi$
$911$	19.7758	−	34.2528i	0.655203	−	1.13484i	0.981843	−	0.189696i	$-0.0607501\pi$
$912$		0			0
$913$	26.8547	+	46.5137i	0.888762	+	1.53938i
$914$	−16.3249	+	21.1393i	−0.539980	+	0.699225i
$915$		0			0
$916$	18.9027	−	4.93977i	0.624561	−	0.163215i
$917$	−22.3001			−0.736414
$918$		0			0
$919$		−	22.7057i		−	0.748991i	−0.927229	−	0.374495i	$-0.877816\pi$
$919$		−	22.7057i		−	0.748991i	0.927229	−	0.374495i	$-0.122184\pi$
$920$	1.61096	−	1.21254i	0.0531118	−	0.0399762i
$921$		0			0
$922$	−16.6868	+	21.6079i	−0.549551	+	0.711618i
$923$	34.9194	−	20.1608i	1.14939	−	0.663599i
$924$		0			0
$925$	17.2954	+	9.98551i	0.568669	+	0.328321i
$926$	3.06388	−	1.25801i	0.100685	−	0.0413406i
$927$		0			0
$928$	40.7246	−	16.1351i	1.33685	−	0.529661i
$929$	−36.0663	−	20.8229i	−1.18330	−	0.683176i	−0.226521	−	0.974006i	$-0.572735\pi$
$929$	−36.0663	−	20.8229i	−1.18330	−	0.683176i	−0.956775	+	0.290830i	$0.906068\pi$
$930$		0			0
$931$	−24.1194	−	41.7760i	−0.790480	−	1.36915i
$932$	2.46992	−	8.99482i	0.0809049	−	0.294635i
$933$		0			0
$934$	−2.30559	+	17.1036i	−0.0754414	+	0.559646i
$935$	−4.86169			−0.158994
$936$		0			0
$937$	54.4421			1.77855			0.889274	−	0.457376i	$-0.151211\pi$
$937$	54.4421			1.77855			0.889274	+	0.457376i	$0.151211\pi$
$938$	9.75882	−	72.3938i	0.318637	−	2.36374i
$939$		0			0
$940$	17.9861	+	4.93887i	0.586643	+	0.161088i
$941$	21.8217	+	37.7963i	0.711368	+	1.23213i	0.964344	+	0.264653i	$0.0852573\pi$
$941$	21.8217	+	37.7963i	0.711368	+	1.23213i	−0.252976	+	0.967473i	$0.581409\pi$
$942$		0			0
$943$	6.34401	+	3.66272i	0.206589	+	0.119274i
$944$	7.01710	+	0.0868604i	0.228387	+	0.00282706i
$945$		0			0
$946$	−29.8704	+	12.2646i	−0.971170	+	0.398755i
$947$	−11.5858	−	6.68905i	−0.376487	−	0.217365i	0.299802	−	0.954002i	$-0.403080\pi$
$947$	−11.5858	−	6.68905i	−0.376487	−	0.217365i	−0.676289	+	0.736637i	$0.736413\pi$
$948$		0			0
$949$	−30.8285	+	17.7989i	−1.00074	+	0.577775i
$950$	−11.2539	+	14.5727i	−0.365123	+	0.472801i
$951$		0			0
$952$	12.6850	−	9.54780i	0.411125	−	0.309446i
$953$		−	36.5239i		−	1.18313i	−0.806259	−	0.591563i	$-0.798511\pi$
$953$		−	36.5239i		−	1.18313i	0.806259	−	0.591563i	$-0.201489\pi$
$954$		0			0
$955$	−21.8422			−0.706796
$956$	1.73209	+	6.62805i	0.0560197	+	0.214366i
$957$		0			0
$958$	−30.6402	+	39.6763i	−0.989940	+	1.28188i
$959$	36.6304	+	63.4458i	1.18286	+	2.04877i
$960$		0			0
$961$	−15.3354	+	26.5617i	−0.494690	+	0.856828i
$962$	−10.6501	−	25.9382i	−0.343372	−	0.836282i
$963$		0			0
$964$	−1.78681	+	1.76483i	−0.0575493	+	0.0568414i
$965$	−0.474833	+	0.822435i	−0.0152854	+	0.0264751i
$966$		0			0
$967$	19.4015	−	11.2015i	0.623911	−	0.360215i	−0.154479	−	0.987996i	$-0.549370\pi$
$967$	19.4015	−	11.2015i	0.623911	−	0.360215i	0.778390	+	0.627781i	$0.216037\pi$
$968$	2.55700	+	20.9214i	0.0821852	+	0.672439i
$969$		0			0
$970$	−10.4220	−	1.40490i	−0.334629	−	0.0451087i
$971$		−	33.7841i		−	1.08418i	−0.840320	−	0.542091i	$-0.817633\pi$
$971$		−	33.7841i		−	1.08418i	0.840320	−	0.542091i	$-0.182367\pi$
$972$		0			0
$973$		−	37.1609i		−	1.19132i
$974$	3.54910	−	26.3282i	0.113720	−	0.843611i
$975$		0			0
$976$	19.4154	+	34.6108i	0.621471	+	1.10786i
$977$	−12.6710	+	7.31560i	−0.405381	+	0.234047i	−0.688803	−	0.724948i	$-0.741864\pi$
$977$	−12.6710	+	7.31560i	−0.405381	+	0.234047i	0.283422	+	0.958995i	$0.408530\pi$
$978$		0			0
$979$	−21.7872	+	37.7365i	−0.696322	+	1.20606i
$980$	−20.5185	+	20.2661i	−0.655440	+	0.647376i
$981$		0			0
$982$	1.60829	−	0.660352i	0.0513226	−	0.0210727i
$983$	−18.8379	+	32.6283i	−0.600837	+	1.04068i	0.391858	+	0.920026i	$0.371832\pi$
$983$	−18.8379	+	32.6283i	−0.600837	+	1.04068i	−0.992695	+	0.120654i	$0.961501\pi$
$984$		0			0
$985$	0.246742	+	0.427370i	0.00786185	+	0.0136171i
$986$	−10.3297	−	7.97715i	−0.328964	−	0.254044i
$987$		0			0
$988$	25.0112	−	6.53610i	0.795712	−	0.207941i
$989$	−3.99001			−0.126875
$990$		0			0
$991$			25.7352i			0.817504i	0.912645	+	0.408752i	$0.134036\pi$
$991$			25.7352i			0.817504i	−0.912645	+	0.408752i	$0.865964\pi$
$992$	3.21114	+	0.473406i	0.101954	+	0.0150307i
$993$		0			0
$994$	−52.2471	−	40.3481i	−1.65718	−	1.27976i
$995$	−0.518666	+	0.299452i	−0.0164428	+	0.00949326i
$996$		0			0
$997$	−33.4015	−	19.2844i	−1.05784	−	0.610743i	−0.133004	−	0.991115i	$-0.542462\pi$
$997$	−33.4015	−	19.2844i	−1.05784	−	0.610743i	−0.924833	+	0.380373i	$0.875796\pi$
$998$	1.86564	+	4.54377i	0.0590558	+	0.143831i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.l.g.107.23		48
3.2	odd	2	inner	648.2.l.g.107.2		48
4.3	odd	2		2592.2.p.g.431.14		48
8.3	odd	2	inner	648.2.l.g.107.18		48
8.5	even	2		2592.2.p.g.431.11		48
9.2	odd	6		648.2.f.c.323.16	yes	24
9.4	even	3	inner	648.2.l.g.539.7		48
9.5	odd	6	inner	648.2.l.g.539.18		48
9.7	even	3		648.2.f.c.323.9	✓	24
12.11	even	2		2592.2.p.g.431.12		48
24.5	odd	2		2592.2.p.g.431.13		48
24.11	even	2	inner	648.2.l.g.107.7		48
36.7	odd	6		2592.2.f.c.1295.11		24
36.11	even	6		2592.2.f.c.1295.13		24
36.23	even	6		2592.2.p.g.2159.11		48
36.31	odd	6		2592.2.p.g.2159.13		48
72.5	odd	6		2592.2.p.g.2159.14		48
72.11	even	6		648.2.f.c.323.10	yes	24
72.13	even	6		2592.2.p.g.2159.12		48
72.29	odd	6		2592.2.f.c.1295.12		24
72.43	odd	6		648.2.f.c.323.15	yes	24
72.59	even	6	inner	648.2.l.g.539.23		48
72.61	even	6		2592.2.f.c.1295.14		24
72.67	odd	6	inner	648.2.l.g.539.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
648.2.f.c.323.9	✓	24	9.7	even	3
648.2.f.c.323.10	yes	24	72.11	even	6
648.2.f.c.323.15	yes	24	72.43	odd	6
648.2.f.c.323.16	yes	24	9.2	odd	6
648.2.l.g.107.2		48	3.2	odd	2	inner
648.2.l.g.107.7		48	24.11	even	2	inner
648.2.l.g.107.18		48	8.3	odd	2	inner
648.2.l.g.107.23		48	1.1	even	1	trivial
648.2.l.g.539.2		48	72.67	odd	6	inner
648.2.l.g.539.7		48	9.4	even	3	inner
648.2.l.g.539.18		48	9.5	odd	6	inner
648.2.l.g.539.23		48	72.59	even	6	inner
2592.2.f.c.1295.11		24	36.7	odd	6
2592.2.f.c.1295.12		24	72.29	odd	6
2592.2.f.c.1295.13		24	36.11	even	6
2592.2.f.c.1295.14		24	72.61	even	6
2592.2.p.g.431.11		48	8.5	even	2
2592.2.p.g.431.12		48	12.11	even	2
2592.2.p.g.431.13		48	24.5	odd	2
2592.2.p.g.431.14		48	4.3	odd	2
2592.2.p.g.2159.11		48	36.23	even	6
2592.2.p.g.2159.12		48	72.13	even	6
2592.2.p.g.2159.13		48	36.31	odd	6
2592.2.p.g.2159.14		48	72.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40154 + 0.188930i) q^{2} +(1.92861 + 0.529584i) q^{4} +(0.474833 + 0.822435i) q^{5} +(4.07898 + 2.35500i) q^{7} +(2.60297 + 1.10660i) q^{8} +O(q^{10})\)	\(q+(1.40154 + 0.188930i) q^{2} +(1.92861 + 0.529584i) q^{4} +(0.474833 + 0.822435i) q^{5} +(4.07898 + 2.35500i) q^{7} +(2.60297 + 1.10660i) q^{8} +(0.510114 + 1.24238i) q^{10} +(-3.72007 - 2.14778i) q^{11} +(-3.52349 + 2.03429i) q^{13} +(5.27191 + 4.07126i) q^{14} +(3.43908 + 2.04272i) q^{16} -1.19178i q^{17} -3.17693 q^{19} +(0.480220 + 1.83762i) q^{20} +(-4.80803 - 3.71303i) q^{22} +(-0.375325 - 0.650083i) q^{23} +(2.04907 - 3.54909i) q^{25} +(-5.32263 + 2.18544i) q^{26} +(6.61959 + 6.70204i) q^{28} +(3.87181 - 6.70617i) q^{29} +(0.496917 - 0.286895i) q^{31} +(4.43407 + 3.51270i) q^{32} +(0.225163 - 1.67032i) q^{34} +4.47293i q^{35} +4.87320i q^{37} +(-4.45258 - 0.600216i) q^{38} +(0.325864 + 2.66622i) q^{40} +(-8.45135 + 4.87939i) q^{41} +(2.65770 - 4.60327i) q^{43} +(-6.03713 - 6.11233i) q^{44} +(-0.403212 - 0.982025i) q^{46} +(4.91012 - 8.50458i) q^{47} +(7.59204 + 13.1498i) q^{49} +(3.54237 - 4.58705i) q^{50} +(-7.87276 + 2.05736i) q^{52} +0.877682 q^{53} -4.07935i q^{55} +(8.01139 + 10.6438i) q^{56} +(6.69348 - 8.66745i) q^{58} +(1.51936 - 0.877204i) q^{59} +(8.59196 + 4.96057i) q^{61} +(0.750651 - 0.308212i) q^{62} +(5.55086 + 5.76090i) q^{64} +(-3.34614 - 1.93189i) q^{65} +(-5.48335 - 9.49744i) q^{67} +(0.631147 - 2.29848i) q^{68} +(-0.845069 + 6.26897i) q^{70} -9.91048 q^{71} +8.74944 q^{73} +(-0.920692 + 6.82996i) q^{74} +(-6.12706 - 1.68245i) q^{76} +(-10.1160 - 17.5215i) q^{77} +(-4.97571 - 2.87273i) q^{79} +(-0.0470178 + 3.79837i) q^{80} +(-12.7667 + 5.24193i) q^{82} +(-10.8283 - 6.25173i) q^{83} +(0.980161 - 0.565896i) q^{85} +(4.59456 - 5.94953i) q^{86} +(-7.30646 - 9.70724i) q^{88} -10.1440i q^{89} -19.1630 q^{91} +(-0.379583 - 1.45252i) q^{92} +(8.48848 - 10.9918i) q^{94} +(-1.50851 - 2.61282i) q^{95} +(-3.91511 + 6.78118i) q^{97} +(8.15614 + 19.8643i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{16} + 12 q^{22} - 24 q^{25} + 24 q^{28} + 24 q^{34} + 24 q^{40} - 24 q^{46} + 24 q^{49} + 12 q^{58} + 48 q^{64} - 48 q^{67} + 36 q^{70} + 60 q^{76} - 72 q^{82} + 60 q^{88} - 48 q^{94}+O(q^{100}) \) 48 * q - 12 * q^16 + 12 * q^22 - 24 * q^25 + 24 * q^28 + 24 * q^34 + 24 * q^40 - 24 * q^46 + 24 * q^49 + 12 * q^58 + 48 * q^64 - 48 * q^67 + 36 * q^70 + 60 * q^76 - 72 * q^82 + 60 * q^88 - 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more